Deriving Discrete Convolution Sums Through Relationships With Ramanujan-Type Eisenstein Series

被引：0

作者：

Chandrashekara, Vidya Harekala ^{[1
]}

Badanidiyoor, Ashwath Rao ^{[2
]}

Bhat, Smitha Ganesh ^{[1
]}

机构：

[1] Manipal Inst Technol, Manipal Acad Higher Educ, Dept Math, Manipal, Karnataka, India

[2] Manipal Inst Technol, Manipal Acad Higher Educ, Select Grade Dept Comp Sci, Manipal, Karnataka, India

来源：

ENGINEERING LETTERS | 2024年 / 32卷 / 07期

关键词：

convolution outcome; algebra; probability theory; numerical analysis; deep learning; CUBIC MODULAR IDENTITIES;

D O I：

暂无

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

This study seeks to establish connections between Ramanujan-type Eisenstein series and Borweins' cubic theta functions, employing the (p, k)-parametrization method introduced by Alaca. Furthermore, the derived identities are applied to provide a novel representation for the evaluation of the discrete convolution sum Sigma(2l+3m=n) delta(i)delta(j).

引用

页码：1500 / 1509

页数：10

共 41 条

[21] Hypergeometric identities for 10 extended Ramanujan-type series
Guillera, Jesus
[J]. RAMANUJAN JOURNAL, 2008, 15 (02): : 219 - 234
[22] Two hypergeometric summation theorems and Ramanujan-type series
Liu, Hongmei
Qi, Shuhua
Zhang, You
[J]. INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 2013, 24 (11) : 905 - 910
[23] On a Ramanujan-type series associated with the Heegner number 163
Campbell, John M.
[J]. JOURNAL OF NUMBER THEORY, 2024, 259 : 322 - 329
[24] More hypergeometric identities related to Ramanujan-type series
Jesús Guillera
[J]. The Ramanujan Journal, 2013, 32 : 5 - 22
[25] Ramanujan type congruences for the Klingen-Eisenstein series
Toshiyuki Kikuta
Sho Takemori
[J]. Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg, 2014, 84 : 257 - 266
[26] Ramanujan type congruences for the Klingen-Eisenstein series
Kikuta, Toshiyuki
Takemori, Sho
[J]. ABHANDLUNGEN AUS DEM MATHEMATISCHEN SEMINAR DER UNIVERSITAT HAMBURG, 2014, 84 (02): : 257 - 266
[27] Cubic modular equations and new Ramanujan-type series for 1/π
Chan, HH
Liaw, WC
[J]. PACIFIC JOURNAL OF MATHEMATICS, 2000, 192 (02) : 219 - 238
[28] Generalizations of Baruah and Berndt?s Ramanujan-type series for 1/?
Campbell, John M.
[J]. NOTE DI MATEMATICA, 2022, 42 (02): : 75 - 92
[29] Rogers–Ramanujan type generalized reciprocal identities and Eisenstein series
Zafer Selcuk Aygin
[J]. Research in Number Theory, 2023, 9
[30] Rogers-Ramanujan type generalized reciprocal identities and Eisenstein series
Aygin, Zafer Selcuk
[J]. RESEARCH IN NUMBER THEORY, 2023, 9 (01)

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